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On the Cubic Lowest Landau Level Equation

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Abstract

We study dynamical properties of the cubic lowest Landau level equation, which is used in the modeling of fast rotating Bose–Einstein condensates. We obtain bounds on the decay of general stationary solutions.We then provide a classification of stationary waves with a finite number of zeros. Finally, we are able to establish which of these stationary waves are stable, through a variational analysis.

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Authors and Affiliations

  1. Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris–Saclay, 91405, Orsay, France

    Patrick Gérard

  2. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012-1185, USA

    Pierre Germain

  3. Institut Élie Cartan, Université de Lorraine, B.P. 70239, 54506, Vandœuvre-lès-Nancy Cedex, France

    Laurent Thomann

Authors
  1. Patrick Gérard
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  2. Pierre Germain
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  3. Laurent Thomann
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Corresponding author

Correspondence to Pierre Germain.

Additional information

Communicated by S. Serfaty

P. Gérard is supported by the Grant “ANAE” ANR-13-BS01-0010-03.

P. Germain is supported by the NSF Grant DMS-1501019.

L. Thomann is supported by the Grants “BEKAM” ANR-15-CE40-0001, “ISDEEC”ANR-16-CE40-0013 and by the ERC Project FAnFAre No. 637510.

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Gérard, P., Germain, P. & Thomann, L. On the Cubic Lowest Landau Level Equation. Arch Rational Mech Anal 231, 1073–1128 (2019). https://doi.org/10.1007/s00205-018-1295-4

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